Question

Express 3.28 bar as rational number in the form of p\q where p and q are integer and q is not equal to 0

Answer 1

let 3.28bar=X X=3.28 bar=3.282828.........

X=3.2828...

multiplying with 100 on both sides

100X=328.2828......

Now equation 2-1

100X =328.2828.....

- X= 3.2828...

99X=325.000....

X=325/99

Therefore 3.28 bar=325/99

Answer 2

$\displaystyle \bf{ 3. \overline{28} = \frac{325}{99} }$

Which is of the form p/q where p , q are integers and q ≠ 0

Given :

The number $\displaystyle \sf{ 3. \overline{28} }$

To find :

To express in the form p/q where p , q are integers and q ≠ 0

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{ 3. \overline{28} }$

Step 2 of 2 :

Express in the form p/q where p , q are integers and q ≠ 0

$\displaystyle \sf{ Let \: \: x = 3. \overline{28} }$

Then x = 3.28282828... - - - - - - - (1)

Multiplying both sides by 100 we get

100x = 328.28282828... - - - - - - (2)

Equation 2 - Equation 1 gives

99x = 325

$\displaystyle \sf{ \implies x = \frac{325}{99} }$

$\displaystyle \sf{ \therefore \: \: 3. \overline{28} = \frac{325}{99}}$

Which is of the form p/q where p , q are integers and q ≠ 0

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